Question: Multiply the following complex numbers, marked as blue dots on the graph: $(3) \cdot ( e^{\pi i / 6})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3$ ) has angle $0$ and radius $3$ The second number ( $ e^{\pi i / 6}$ ) has angle $\frac{1}{6}\pi$ and radius $1$ The radius of the result will be $3 \cdot 1$ , which is $3$ The angle of the result is $0 + \frac{1}{6}\pi = \frac{1}{6}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{1}{6}\pi$.